Is there any scientific/mathematical argument that prevents deep learning from ever producing strong AI?
Judea Pearl's 2018 comment on ACM.org, in his To, Build Truly Intelligent Machines, Teach Them Cause and Effect is piercing truth.

All the impressive achievements of deep learning amount to just curve fitting.

It may be less sensational and more technically correct to state that it is not, &quot;Just curve fitting,&quot; but rather, &quot;sophisticated surface fitting.&quot; Nonetheless, his general assessment indicates the need to look beyond tuning nonlinear functions to fit a surface in $\mathbb{R}^n$ and consider whether cognition is achievable with a deep network. The split in answers to this question is odd. We have two conflicting assertions, often strongly stated.

Artificial networks cannot perform logic.
Artificial networks are the best approach to AI.

How can rationality be excluded from the list of important human features of intelligence, which is what these two assertions are taken together would mean?
Is the human brain a network of sophisticated curve fitters?  Marvin Minsky's famous quote, &quot;The brain happens to be a meat machine,&quot; was offered without proof, and neither a proof of his trivialization of the human brain nor a proof that the brain is beyond the reach of Turing computability has been offered since.
When you read these words, are your neural networks doing the following sequence of curve fits?

Edges from retinal rods and cones
Lines from edges
Shapes from lines
Letters from shapes
Linguistic elements from groups of letters
Linguistic structures from elements
Understanding from linguistic structures

The case is strong for the affirmation that the first five is a convergence mechanism on a model, and all the machine learning structure is just a method to fit the data to the model.
Those last two bullet items are where the paradigm breaks down and where many AI researchers and authors have correctly stated that machine learning has significant limitations when based solely on layers of multi-layer perceptrons and convolution kernels.  Furthermore, the last bullet item is grossly oversimplified in its current state, probably by orders of magnitude.  Even if Minsky is correct that a computer can perform what the brain does, the process of reading and understanding this paragraph could easily have a thousand different kinds of unique process components in patterns of internal workflow with massive parallelism.  Imaging technology indicates this probability.  We have computers modelling only the simplest peripheral layers.

Is there any scientific/mathematical argument that prevents deep learning from ever producing strong AI? — No. But there is no such argument that guarantees it either.

Other questions here investigate whether these sophisticated curve fitters can perform elements of cognition or reasoning.

Could a neural network detect primes?
Can neural networks be used to prove conjectures?

The totem of three in the question's image, seeing, doing, and imagining, is not particularly complete, accurate, or insightful.

There are at least five sensory paradigms in humans, not one
Doing preceded human senses by billions of years — bacteria do
Imagining is not a significantly higher process than scenario replay from models of past experience with some method to apply set functions to combine them and inject random mutations
Creativity may just be imagining in the previous bullet item followed by weeding out useless imagination results with some market-oriented quality criteria, leaving the impressive creative products that sell

The higher forms are appreciation, a sense of realities beyond the scope of scientific measurement, legitimate doubt, love, sacrifice for the good of others or humanity.
Many recognize that the current state of AI technology is nowhere near the procurement of a system that can reliably answer, &quot;How can I make Y happen?&quot; or &quot;If I have acted differently, will X still occur?&quot;
There is no mathematical proof that some combination of small curve fitting elements can or cannot achieve the ability to answer those questions as well a typical human being can, mostly because there is insufficient understanding of what intelligence is or how to define it in mathematical terms.
It is also possible that human intelligence doesn't exist at all, that references to it are based on a religious belief that we are higher as a species than other species.  That we can populate, consume, and exterminate is not actually a very intelligent conception of intelligence.
The claim that human intelligence is an adaptation that differentiates us from other mammals conflicts with whether we adapt well.  We have not been tested.  Come the next meteoric global killer with a shock wave of the magnitude of that of the Chicxulub crater's meteor, followed by a few and a thousand years of solar winter and we'll see whether it is our 160,000-year existence or bacteria's 4,000,000,000 year existence that proves more sustainable.  In the timeline of life, human intelligence has yet to prove itself significant as an adaptive trait.
What is clear about AI development is that other kinds of systems are playing a role along with deep learners based on the multi-layer perceptron concept and convolution kernels which are strictly surface fitters.
Q-learning components, attention-based components, and long-short term memory components are all strictly a surface fitter too, but only by stretching the definition of surface fitting considerably.  They have real-time adaptive properties and state, so they can be Turing complete.
Fuzzy logic containers, rules-based systems, algorithms with Markovian properties, and many other component types also play their role and are not surface fitters at all.
In summary, there are points made that have a basis in more than plausibility or a pleasing intuitive quality, however, many of these authors do not provide a mathematical framework with definitions, applications, lemmas, theorems, proofs, or even thought experiments that can be scrutinized in a formal way.